A compact, ultrashort, laser-based hard X-ray source particularly suited for high repetition rate laser systems (≥1 kHz) is presented. X rays in the keV energy range are generated efficiently with 30 fs laser pulses on different tape targets containing chromium and iron. Spectroscopic investigations showed that for the chromium as well as for the iron tapes, strong Ka and Kb emission were observed in addition to a weak bremsstrahlung continuum. These tape targets are especially suited for applications in a transmission geometry, which provides significant advantages. The operation of the tape target was studied with repetition rates up to 10 kHz. With input pulses of 0.5 mJ and modest intensities in the low 10 15 W/cm 2 range, X-ray Ka photon fluxes exceeding 6 × 10 9 photons/s were achieved, yielding conversion efficiencies of h Ka > 10 −6 . With a toroidally bent crystal the generated radiation was monochromatized and focused to a 85-µm diameter spot demonstrating the ability of the source to act as a X-ray point source, a pre-requisite for an application in X-ray microscopy.